Carve Alpha Channel from Plane
You could make 2 planes. One with a displace texture and subsurf modifiers applied.



On the other plane add subsurf and a boolean modifiers to receive the displace mesh as a hole cutter.



Boolean modifier will need a large amount of subsurf to get clean holes, but you could use a decimate modifier and smooth modifier to relax the mesh and reduce the vertices count.





Here I have also added a solidify modifier to make the plane thick.